United play City at Old Trafford on Wednesday and taking any points off them will hand the Reds the advantage in a hard-fought title race.
Per Goal, Walker said:
"United fans are in a difficult situation obviously.
"When I'm out and about or walking my dogs, United fans are coming up to me saying, 'We'd rather City win the league than Liverpool.'
"It's strange to hear, but I can assure you the United players aren't going to leave a red carpet and say, 'Go on City, score past us.'
"They're going to make it difficult because it's a game of football and they're fighting for the top four as well. so they need the points."
City are two points behind Liverpool with four matches to play, while the Reds have three games left. To keep the race in their own hands and guarantee the title, the Sky Blues must win all of their remaining fixtures.
Neither side has dropped any points of late, as The Independent's Miguel Delaney observed:
It all makes for an unwelcome scenario for United fans, who will be forced to watch one of their most bitter rivals lift the Premier League trophy at the end of the season.
Beating or drawing with City on Wednesday will swing the race in Liverpool's favour, though on current form that will be a difficult task for United.
The Red Devils have lost six of their last eight matches in all competitions and were humiliated 4-0 by Everton on Sunday.
ESPN's Rob Dawson pulled no punches in his assessment of United's performance, while James Robson of the Evening Standard would not be surprised if things got worse against the Sky Blues:
Away from the title race, United also have to worry about their own bid to qualify for next season's UEFA Champions League by finishing in the top four.
The Red Devils will kick off their clash with City in sixth, three points behind fourth-place Chelsea, who have played one match more.
United will play the Blues after facing City in a game that's likely to have a significant impact on their respective top-four bids.
If they're to realistically overhaul both Chelsea and fifth-place Arsenal—who are two points ahead and have played the same number of games—though, they need to stop the rot with a result against City.